1. (30 points) Solve the life-cycle optimal choice for a consumer whose endowment is given (100, 50) and faces a perfect capital market with interest rate of 10%, if the period utility function is v(x) = ln x and Beta (B) = 0.9. (report it up to two decimal places).

2. Answer the following questions:

a) How would you expect an inflation-targeting central bank to respond to a fall in world trade? Explain the central bank's reasoning. (3 points)

b) Does the exchange rate overshoot as a consequence of the central bank's actions? Justify your answer. (2 points)